## Group theory and general relativity: representations of the Lorentz group and their applications to the gravitational field |

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### Contents

The Rotation Group | 1 |

The Lorentz Group | 19 |

Spinor Representation of the Lorentz Group | 34 |

Copyright | |

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### Common terms and phrases

Acad algebra arbitrary asymptotic BMS group called Carmeli Chapter commutation complementary series complex numbers components condition conjugate constant coordinate system coordinate transformation corresponding defined denoted differential discussed E. T. Newman eigenvalue Einstein Einstein field equations equation of motion equivalent finite-dimensional follows geodesic rays given by Eq gravitational field gravitational field equations gravitational radiation group 03 group SL(2 group SU2 Hence Hermitian Hilbert space infinitesimal operators integral irreducible representation Kerr metric Lemma linear Lorentz group Lorentz transformation M. A. Naimark Math matrix elements matrix g metric tensor null Nuovo Cim obtains operator D(g orthochronous orthogonal parameter particles Phys physical polynomial principal series Problem Proc Prove Eqs relation relativity representations D(g Riemann tensor satisfy scalar product Schwarzschild metric Show sin2 space D(x space-time spherical spin coefficients spinor representation subgroup subspace symmetric tetrad theorem tion unitary representations vanish variables vector Weyl spinor Weyl tensor Yang-Mills field